Einstein almost cokähler manifolds

2014/09/15 by Conti, Diego, Fernández, Marisa
#53C15 (Secondary) #53C25 (Primary) #53D15 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1409.4437

Abstract

We study an odd-dimensional analogue of the Goldberg conjecture for compact Einstein almost Kähler manifolds. We give an explicit non-compact example of an Einstein almost cokähler manifold that is not cokähler. We prove that compact Einstein almost cokähler manifolds with non-negative *-scalar curvature are cokähler (indeed, transversely Calabi-Yau); more generally, we give a lower and upper bound for the *-scalar curvature in the case that the structure is not cokähler. We prove similar bounds for almost Kähler Einstein manifolds that are not Kähler.

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